A Mathematical Model Water Movement about Bottom-Water-Drive Reservoirs

This paper presents tbe development and solution of a mathematical model for aquifer water movement about bottom-water-drive reservoirs. Pressure gradients in the vertica2 direction due to water /low are taken into account, A vertical permeability equal to a fraction of the borizorztal permeability is also included in tbe model. The solution is given in the /orm o~ a dimensionless pressure-drop quarztity “tabulated as a function of dimensionless time. This quantity can be used in given equations to compute reservor? pressure irom a known water-inf Iux rat e, to predictwater-infkv rate (or cumulrrtiwe amount) from a reservoir-pressure schedule or to predict gas reservoir pressure and pore-volume performance from a given gas-in-place schedule. Tbe model is applied in example problems to gas-storage reser~ voirs, and the difference between resewoir per@rmances predicted’ by tbe thick sand model of this paper and tbe horizontal, radial-flow model is shown to be appreciable,